Heat 3 tablespoons of the oil in a large frying pan (not nonstick) over medium-high heat until shimmering. Add the potatoes and season with salt. Cook, occasionally tossing and scraping up any browned bits from the bottom of the pan with a flat metal spatula, until the potatoes are beginning to brown in spots, about 6 minutes. Scrape the potatoes into a medium bowl and set aside.

Reduce the heat to medium, add the remaining tablespoon of oil to the pan, and heat until shimmering. Add the mustard seeds and toast until fragrant and popping, about 1 minute. Add the ginger, garlic, cumin, measured salt, coriander, turmeric, and cayenne and cook, stirring occasionally with a wooden spoon, until fragrant, about 1 minute.

Add the cauliflower and stir to coat in the spices. Return the potatoes to the pan, add the water, and stir to combine. Cover with a tightfitting lid and cook until the cauliflower is tender, about 10 minutes. Add the butter and stir until it is melted and coating the vegetables. Taste and season with salt as needed.